cp's OEIS Frontend

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122202 with the recursion scheme "KROF", or equivalently row n is obtained as KROF(KROF(n-th row of A089840)). See A122202 for the description of KROF. Each row occurs only once in this table. Inverses of these permutations can be found in table A122289.

This is the signature-permutation of Catalan automorphism which is derived from the automorphism *A123492 with the recursion schema KROF (defined in A122202). Like automorphisms *A057163 and *A069767/*A069768 these automorphisms are closed with respect to the subset of "zigzagging" binary trees (i.e., those binary trees where there are no nodes with two nonempty branches, or equivalently, those ones for which Stanley's interpretation (c) forms a non-branching line) and thus induce a permutation of binary strings. That is, starting from the root of such a binary tree, the turns taken by nonempty branches are interpreted as binary digits 0 or 1, depending on whether the tree grows to the left or right. In this manner, the Catalan automorphisms *A123494 and *A123493 induce the Binary Reflected Gray Code (see A003188 and A006068).

The signature-permutation of the automorphism which is derived from the first non-recursive automorphism *A069770 with recursion schema NEPEED (see A122284 for the definition), or equivalently, derived from the fifteenth non-recursive automorphism *A089859 with recursion schema KROF (see A122202 for the definition).

The signature-permutation of the automorphism which is derived from the 21st non-recursive automorphism *A089863 with recursion schema KROF (see A122202 for the definition).

The signature-permutation of the automorphism which is derived from the seventh non-recursive automorphism *A089854 with recursion schema KROF (see A122202 for the definition).

The signature-permutation of the automorphism which is derived from the third non-recursive automorphism *A089850 with recursion schema KROF (see A122202 for the definition).

The signature-permutation of the automorphism which is derived from the tenth non-recursive automorphism *A089856 with recursion schema KROF (see A122202 for the definition).

The signature-permutation of the automorphism which is derived from the ninth non-recursive automorphism *A089855 with recursion schema KROF (see A122202 for the definition).

The signature-permutation of the automorphism which is derived from the eighteenth non-recursive automorphism *A089861 with recursion schema KROF (see A122202 for the definition).

The signature-permutation of the automorphism which is derived from the nineteenth non-recursive automorphism *A073270 with recursion schema KROF (see A122202 for the definition).